Adding a documentation reference for a custom Object attribute
bpy.data.*  has attributes like objects, meshes, speakers, cameras etc.  None of these collections have a RigProps pointer property.  Use the type that the custom property has been registered on.

Small example, Object has an IntProperty named "example" registered.  Added UI in object properties name panel to test. 

import bpy
from bpy.props import IntProperty
bpy.types.Object.example = IntProperty()

def draw(self, context):
    self.layout.prop(context.object, "example")

def my_addon_docs():
    map = (
        ("bpy.types.Object.example",    "/posing/"),
    )  
    return "https://some.website", map

bpy.types.OBJECT_PT_context_object.append(draw)
bpy.utils.register_manual_map(my_addon_docs)


In your case, I'd suggest using the map 

    map = (
        ("bpy.types.Object.RigProps.*",    "/posing/"),
    )  
    return "https://some.website", map


Or if you have anchors (or query strings)

def my_addon_docs():
    props = ("use_xxx", "use_yyy", "use_zzz")
    map = [
        ("bpy.types.Object.RigProps.%s" % prop,    
          "#%s" % prop) for prop in props]
    return "https://some.website/posing", map